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Angle Bisector Theorem: In triangle PQR, the angle bisector from vertex P divides the opposite side QR into segments x and y proportional to the adjacent sides a and b.

Diagram illustrating the Angle Bisector Theorem, showing triangle PQR with point S on QR, where PS is the angle bisector of angle P, and the ratio a/b = x/y.

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(view all bisector geometry)